Laptop keeps shutting down itself.

Hey first of all im sorry for being away for such a long time and not replying to anyone or posting anything. (Ill try to post replies more often now). Anyway, I have a laptop,
it's a Aspire 5720, 2gb ram, 160gb hdd and intel 2 duo core processor, windows xp pro.

The problem is that whenever i try to run something like the internet, or a game or just leave it idle for somtime, probaly every 2nd day or randomly it shuts down, also my mouse crusor moves like from one spot to another (verry little), and suppose if i am trying to
type in my name, sometimes when i type in a r it would change to another letter or number.....
I have scaned my laptop with zone alarm Antivirus, Avg free, ClamWin, or SpyBot and norton antivirus 2009, it has dectedted nothing so far, but i am worried if there is a hidden virus or backdoor server somewere, which when i go to the task manager, all i find is the system processes or some processes with my name next to it.
I am having this problem for like about a month now or even last year for a while.
Plesase Help me out!!!